Question: Which of the following numbers is a multiple of 9? ${50,53,89,114,117}$
Solution: The multiples of $9$ are $9$ $18$ $27$ $36$ ..... In general, any number that leaves no remainder when divided by $9$ is considered a multiple of $9$ We can start by dividing each of our answer choices by $9$ $50 \div 9 = 5\text{ R }5$ $53 \div 9 = 5\text{ R }8$ $89 \div 9 = 9\text{ R }8$ $114 \div 9 = 12\text{ R }6$ $117 \div 9 = 13$ The only answer choice that leaves no remainder after the division is $117$ $ 13$ $9$ $117$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $9$ are contained within the prime factors of $117$ $117 = 3\times3\times13 9 = 3\times3$ Therefore the only multiple of $9$ out of our choices is $117$. We can say that $117$ is divisible by $9$.